Related papers: Feuilletages en droites, \'{e}quations des eikonal…
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the…
In this paper, we study unirational differential curves and the corresponding differential rational parametrizations. We first investigate basic properties of proper differential rational parametrizations for unirational differential…
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…
Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context…
We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…
We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity results for the stress field. All our results are new even in…
We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.
We prove a version of the variational Euler-Lagrange equations valid for functionals defined on Fr\'echet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.
The solution of the Ornstein-Zernike equation with various closure approximations is studied. This problem is rewritten as an integral equation that can be solved iteratively on a grid. The convergence of the fixed point iterations is…
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…
In this paper, we study nonlinear differential equations arising from Eulerian polynomials and their applications. From our study of nonlinear differential equations, we derive some new and explicit identities involving Eulerian and…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear differential equations. It allows one to express exact solutions…
We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of…
We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions…
The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…
We present a family of fast and accurate Dijkstra-like solvers for the eikonal equation and factored eikonal equation which compute solutions on a regular grid by solving local variational minimization problems. Our methods converge…
Einstein's equations for stationary axisymmetric fields are reformulated as the equations for affine geodesics in a two--dimensional space. The affine collineations of this space are investigated and used to relate explicit solutions of…